A dynamic applet for the exploration of the concept of the limit of a sequence

References

• Tall D, Vinner S. Concept image and concept definition in mathematics with particular reference to limits and continuity. Educ Stud Math. 1981;12(2):151–169.
   Google Scholar
• Tall D. The transition to advanced mathematical thinking: functions, limits, infinity and proof. In: Grouws DA, editor. Handbook of research on mathematics teaching and learning. New York, NY: Macmillan; 1992. p. 495–511.
   Google Scholar
• Roh KH. An empirical study of students understanding of a logical structure in the definition of limit via the ϵ-strip activity. Educ Stud Math. 2010;73:263–279.
   Web of Science ®Google Scholar
• Mamona-Downs J. Letting the intuitive bear on the formal; a didactical approach for the understanding of the limit of a sequence. Educ Stud Math. 2001;48:259–288.
   Google Scholar
• Cory B, Garofalo J. Using dynamic sketches to enhance preservice secondary mathematics teachers’ understanding of limits of sequence. J Res Math Educ. 2011;42(1):65–96.
   Web of Science ®Google Scholar
• Cottrill J, Dubinsky E, Nichols D, Schwingendorf K, Thomas K, Vidakovic D. Understanding the limit concept: beginning with a coordinated process schema. J Math Behav. 1996;15(2):167–192.
   Google Scholar
• Pinto M, Tall D. Student constructions of formal theory: giving and extracting meaning. In: Zaslavsky O, editor. Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education; 1999 Jul 25; Haifa (Israel): Israel Institute of Technology; 1999.
   Google Scholar
• Swinyard C. Reinventing the formal definition of limit: the case of Amy and Mike. J Math Behav. 2011;30(2):93–114.
   Google Scholar
• Cory B, Smith KW. Delving into limits of sequences. Math Teach. 2011;105(1):48–55.
   Google Scholar
• Roh KH. Students’ images and their understanding to definitions of the limit of a sequence. Educ Stud Math. 2008;69(3):217–233.
   Google Scholar
• Roh KH. How to help students conceptualize the rigorous definition of the limit of a sequence. Probl Resour Issues Math Undergraduate Stud. 2010;20(6):473–487.
   Google Scholar
• Davis RB, Vinner S. The notion of limit: some seemingly unavoidable misconception stages. J Math Behav. 1986;5:284–303.
   Google Scholar
• Plass JL, Homer BD, Hayward EO. Design factors for educationally effective animations and simulations. J Comput Higher Educ. 2009;21(1):31–61.
   Google Scholar
• Kidron I, Zehavi N. The role of animation in teaching the limit concept. Int J Comput Algebra Math Educ. 2002;9(3):205–222.
   Google Scholar
• Roh KH, Lee YH. Development of students’ understanding of the logic in the epsilon-N definition of limit. In: Ubuz B, editor. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education; 2011 Jul 10; Ankara (Turkey): Middle East Technical University; 2011.
   Google Scholar
• Leung A. An epistemic model of task design in dynamic geometry environment. ZDM – Int J Math Educ. 2011;43:325–336.
   Google Scholar
• Bartolini Bussi MG, Mariotti MA. Semiotic mediation in the mathematics classroom: artifacts and signs after a Vygotskian perspective. In: English L, editor. Handbook of international research in mathematics education. 2nd ed. New York: Routledge; 2008. p. 750–787.
   Google Scholar
• Mariotti MA. ICT as opportunities for teaching-learning in a classroom: the semiotic potential of artefacts. In: Tso TY, editor. Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education; 2012 Jul 18; Taipei (Taiwan). Wesley Girls High School; 2012.
   Google Scholar
• Bartolini Bussi MG. Verbal interaction in mathematics classroom: a Vygotskian analysis. In: Steinbring H, Bartolini Bussi MG, Sierpinska A, editors. Language and communication in mathematics classroom. Reston, VA: NCTM; 1998. p. 65–84.
   Google Scholar
• Drijvers P, Boon P, Doorman M, Bokhove C, Tacoma S. Digital design: RME principles for designing online tasks. In: Margolinas C, editor. Task design in mathematics education: proceedings of ICMI Study 22. Oxford: University of Oxford; 2013. p. 53–60.
   Google Scholar
• Margolinas C, editor. Task design in mathematics education. Proceedings of ICMI Study 22; 2013 Jul 22; Oxford: University of Oxford.
   Google Scholar